Another way to explain it:

There are two sources of force in the system. The plane engine, and the treadmill. The plane engine pushes forward, and the treadmill pushes backward. The wheels of the plane are the interaction between the two forces, and by rotating they allow the engines to move the plane forward and the treadmill to move itself backward without canceling, by rotating at the sum of the two speeds.

Under interpretation #1, the speed of the treadmill is automatically set to equal the speed of the wheels. This is only true if the engines supply no force to the system, but the question precludes that.

hehehee...I was in meetings most of the day but I checked on this thread a few times. I must say, my head exploded a long time ago. You people be too damn smart for me! :p

This has ceased being a physics discussion and become a semantics issue, hasn't it?

The question does not reference wheel speed, but plane speed. The question is what the plane speed is measured relative to. You can get two different answers, depending on what plane speed is measure relative to. The speed of the plane can be desribed two different ways. They aren't exchangable. The plane isn't on the ground. It's on the treadmill. The treadmill either cancels it’s relative motion, or has no effect whatsoever. See above. No, I’m not saying that. (The forward motion of the aircraft relative to what?) I'm not asking you to do that.
It doesn't hold the plane back, the plane is moving at exactly the speed the treadmill is moving, in the opposite direction.
The question doesn’t include wheel speed as a variable, only plane speed and treadmill speed. No kidding.
The question doesn’t include wheel speed as a variable, only plane speed and treadmill speed.

No, the treadmill stated in the question only cares about the plane speed, never the wheel speed.

Flint, think about the rotation of the Earth being the same as a giant treadmill, can a plane taking off to the west leave the ground?

Q: Does the treadmill have it's own atmosphere?
A: Not as stated in this question.

Good point. The question doesn't clearly state that there is an atmosphere, so a plane wouldn't work anyway. No lift in a vacuum.

The Earth has an atmosphere, the treadmill doesn't, IE, the atmosphere isn't relative to the treadmill, as in 9ths "Earth treadmill" question.

Yes, but the question doesn't state this treadmill is on the Earth, does it?

Umm ... isn't this solely about the action of the plane's engines and the fact that they push air through at great speed (science pushes, but it never, ever sucks:D ), creating air flow over and under the wings, and then the whole Bernoulli effect thing happens, and you get lift? So the treadmill plane should lift off ...

Am I remembering Physics 100 correctly?

otoh, will just the movement of air through the engines provide enough airflow to create sufficient lift for the plane to take off? Normally there's the engine push-through of air plus air passing over/under the wings because the plane is moving relative to the atmosphere - on the treadmill it's not. Will there be enough air moving over the wings to create the needed lift? :confused:

Now if we could just get planes to land on little bitty treadmills, we wouldn't have to build long runways anymore!

Of course not... the air moving across the wing gives lift (a very simplistic description, at-best). The treadmill negates that.

We all have been assuming that the air does not accelerate with the treadmill, which is correct. It is also why the treadmill has no effect. The jet engines push against the AIR, nothing else, so if the air does not accelerate with the treatmill then there must be a constant force pushing back on the aircraft (basic physics). Since the treadmill is only in contact with the wheels, and the wheels cannot transmit a force back onto the aircraft (no brakes being applied), there is an unballenced force acting on the body of the plain. Therefore, the plane must accelerate.

I didn't say it did. I said that wheel speed is identical to the speed of the plane relative to the treadmill.
Again, I didn't say they were. I said that they were different, and that the latter doesn't affect the former.
It cannot cancel the relative motion, because it doesn't apply any force to the plane, just the wheel. The only force pushing the plane is the engine, the engine acts relative to the air, which is not affected by the treadmill. Therefore the plane moves forward relative to the ground.
You say that a lot, but it is irrelevant. Wheel speed is equal to the speed of the plane relative to the treadmill. They are identical.

It would if it kept the plane stationary relative to the ground, which it can't.

Jet engines don't push against the air, they push against the plane. The plane will be pushed forward until it reaches takeoff velocity, no matter what speed the wheels are turning. All they do is keep the plane from dragging on the ground. Planes take off from runways that are moving at 1000 mph, under them, every day. ;)
So a man can tip open a lid that would be to heavy to lift.